In the present estimations, there is only one model parameter \(\alpha \)  introduced by the form factor. As indicated in Ref. [1]} the cutoff \(\Lambda \)  in the form factor should not be far away from the mass of the exchanged meson. The model parameter \(\alpha \)  is expected to be of order unity and usually depends on particular processes  [1]}. Actually, the model parameter \(\alpha \)  can not be estimated from the first principle. It is usually determined by comparing the theoretical estimations with the corresponding experimental data, and check the reasonability of the determined parameter range. However, as for the processes involved in the present work, there are no direct measurements for \(Z_b^{(\prime )} \rightarrow \Upsilon _J(1D) \pi \) . As indicated in the introduction, only the branching ratios of \(\Upsilon (5S) \rightarrow \Upsilon _J(1D) \pi ^+ \pi ^-\)  can be obtained from the experimental data. According to our analysis, we find that the cascade decays \(\Upsilon (5S) \rightarrow Z_b^{(\prime )} \pi \rightarrow \Upsilon (1D) \pi ^+ \pi ^-\)  play essential roles in understanding the large branching ratios of \(\Upsilon (5S) \rightarrow \Upsilon (1D)\pi ^+ \pi ^-\) . Together with the decay processes \(\Upsilon (5S)\rightarrow Z_b^{(\prime )} \pi \) , we can roughly estimate the branching ratios of \(\Upsilon (5S) \rightarrow \Upsilon (1D) \pi ^+ \pi ^-\) , which can be compared with the corresponding experimental data.
